In recent years there has been a great deal of new activity at the interface of biology and computation. This has largely been driven by the massive in flux of data from new experimental technologies, particularly ...

Consider the unnormalized Ricci flow ...Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times ... then the solution can be extended beyond T. In the thesis we prove that ...

(cont.) yield a new proof of a result of Mochizuki yield a new proof of a result of Mochizuki Frobenius-unstable bundles for C general, and hence obtaining a self-contained proof of the resulting formula for the degree of V₂.

In this thesis, the Hilbert scheme of lines on smooth hypersurfaces is studied. The main result is that the Hilbert scheme of lines on any smooth Fano hypersurface of degree d =/< 6 in ... has the expected dimension 2n - ...

In this thesis we explore some of the relatively new approaches to the problem of list-coloring graphs. This is a problem that has its roots in classical graph theory, but has developed an entire theory of its own, that ...

In this thesis, I studied the stability of local complex'singularity exponents (lcse) for holomorphic functions whose zero sets have only isolated singularities. For a given holomorphic function f defined on a neighborhood ...

Chromatic localization can be seen as a way to calculate a particular infinite piece of the homotopy of a spectrum. For example, the (finite) chromatic localization of a p-local sphere is its rationalization, and the ...

We show that for a large class of torsionfree classifying spaces, K-theory filtered ring is an invariant of the genus. We apply this result in two ways. First, we use it to show that the powerseries ring on n indeterminates ...

Given a Galois cover of curves X --> Y with Galois group G which is totally ramified at a point x and unramified elsewhere, restriction to the punctured formal neighborhood of x induces a Galois extension of Laurent series ...

The Minimal Model Program (in short, MMP) aims at classifying projective algebraic varieties from a birational point of view. That means that starting from a projective algebraic variety X, [Delta] it is allowed to change ...

The category of Segal spaces was proposed by Charles Rezk in 2000 as a suitable candidate for a model category for homotopy theories. We show that Quillen functors induce morphisms in this category and that the morphisms ...